Question

given the function $f(x) = x^2 - 9x + 15$, determine the average rate of change of the function over the interval $2 \leq x \leq 9$.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Calculate $f(9)$

$f(9) = 9^2 - 9(9) + 15 = 81 - 81 + 15 = 15$

Step3: Calculate $f(2)$

$f(2) = 2^2 - 9(2) + 15 = 4 - 18 + 15 = 1$

Step4: Compute average rate of change

$\frac{f(9)-f(2)}{9-2} = \frac{15-1}{7} = \frac{14}{7} = 2$

Answer:

2